To solve the equation [tex]\(\frac{4}{17} = \frac{E}{2}\)[/tex] for [tex]\(E\)[/tex], follow these steps:
1. Understand the equation:
The given equation is [tex]\(\frac{4}{17} = \frac{E}{2}\)[/tex]. This is a proportion where two ratios are set equal to each other.
2. Cross-multiplication:
To solve for [tex]\(E\)[/tex], we can use the technique of cross-multiplication. Cross-multiplying the fractions involves multiplying the numerator of each fraction by the denominator of the other fraction. The equation will be:
[tex]\[
4 \cdot 2 = 17 \cdot E
\][/tex]
3. Simplify the equation:
On the left side, multiply 4 by 2:
[tex]\[
8 = 17E
\][/tex]
4. Solve for [tex]\(E\)[/tex]:
To isolate [tex]\(E\)[/tex], divide both sides of the equation by 17:
[tex]\[
E = \frac{8}{17}
\][/tex]
5. Final value:
The exact value of [tex]\(E\)[/tex] is:
[tex]\[
E = \frac{8}{17}
\][/tex]
6. Convert to decimal (if needed):
Converting [tex]\(\frac{8}{17}\)[/tex] to its decimal form, we get approximately:
[tex]\[
E \approx 0.47058823529411764
\][/tex]
So, the solution to the equation [tex]\(\frac{4}{17} = \frac{E}{2}\)[/tex] is [tex]\(E \approx 0.47058823529411764\)[/tex].
